Lambda Definability with Sums via Grothendieck Logical Relations (1999) [6 citations — 0 self]
http://www.cogs.susx.ac.uk/users/marcelo/papers/Ty
http://www.cl.cam.ac.uk/~mpf23/papers/Types/glr.ps
http://www.dcs.ed.ac.uk/~als/Research/glr.ps.gz
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author = {Marcelo Fiore and Alex Simpson},
title = {Lambda Definability with Sums via Grothendieck Logical Relations},
year = {1999}
}
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Abstract:
. We introduce a notion of Grothendieck logical relation and use it to characterise the definability of morphisms in stable bicartesian closed categories by terms of the simply-typed lambda calculus with finite products and finite sums. Our techniques are based on concepts from topos theory, however our exposition is elementary. Introduction The use of logical relations as a tool for characterising the -definable elements in a model of the simply-typed -calculus originated in the work of Plotkin [10], who obtained such a characterisation of the definable elements in the full type hierarchy using a notion of Kripke logical relation. Subsequently, the more general notion of a Kripke logical relation of varying arity was developed by Jung and Tiuryn, and shown to characterise the definable elements in any Henkin model [4]. Although not emphasised in [4], relations of varying arity are powerful enough to characterise relative definability with respect to any given set of elements consider...
Citations
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